| Exam Board | OCR |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Inequalities |
| Type | Compound inequality with double bound |
| Difficulty | Easy -1.2 This is a straightforward C1 question testing basic inequality manipulation. Part (i) requires simple linear operations (subtract 7, divide by 6) on a compound inequality, and part (ii) involves rearranging to x² > 16 and taking square roots. Both are routine textbook exercises with no problem-solving or conceptual challenges beyond direct application of standard techniques. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable |
| Answer | Marks | Guidance |
|---|---|---|
| \(-42 < 6x < -6\) | M1 | 2 equations or inequalities both dealing with all 3 terms |
| \(-7 < x < -1\) | A1, A1 [3] | \(-7\) and \(-1\) seen; \(-7 < x < -1\) (or \(x > -7\) and \(x < -1\)) |
| Answer | Marks | Guidance |
|---|---|---|
| \(x^2 > 16\) | B1 | \(\pm 4\) seen |
| \(x > 4\) | B1 | |
| or \(x < -4\) | B1 [3] | \(x < -4\) not wrapped, not 'and' |
## Question 8:
### Part (i):
$-42 < 6x < -6$ | M1 | 2 equations or inequalities both dealing with all 3 terms
$-7 < x < -1$ | A1, A1 [3] | $-7$ and $-1$ seen; $-7 < x < -1$ (or $x > -7$ and $x < -1$)
### Part (ii):
$x^2 > 16$ | B1 | $\pm 4$ seen
$x > 4$ | B1 |
or $x < -4$ | B1 [3] | $x < -4$ not wrapped, not 'and'
---8 Solve the inequalities\\
(i) $- 35 < 6 x + 7 < 1$,\\
(ii) $3 x ^ { 2 } > 48$.\\
$9 \quad A$ is the point $( 4 , - 3 )$ and $B$ is the point $( - 1,9 )$.\\
\hfill \mbox{\textit{OCR C1 2009 Q8 [6]}}